Measuring Human Rights: High School Mathematics Unit
Note: The next two lessons focus on the Body Mass Index (BMI) as one of the indicators used by the UN to evaluate the degree to which certain populations have adequate food. Be aware that many students may have low self-esteem due to their body weight. This lesson does not focus on issues of obesity and students will not be asked to measure their own weight or calculate their BMI. Rather, we will explore this issue from a population health perspective. The notion of standard weight for children and the classification for BMI are useful as indicators for evaluating populations, not individuals.
In the previous lessons, we focused on the weight of children under five years of age as an indicator for malnutrition (thus lack of adequate food for a population). In this lesson, we examine the BMI of adults in which BMI<18.5 is an indicator of underweight. The notion of BMI has several limitations, which are discussed in the lesson.
Prior knowledge required for the unit
- The ability to convert between U.S. and SI
- The ability to solve two variable equations
- An understanding of percent
Learning Objectives
Students will be able to:
- Understand the function, and calculate the value of BMI.
- Create a two-way frequency table from two categorical variables; read and interpret data displayed in a two-way table.
- Write clear summaries of data displayed in a two-way frequency table.
- Use BICC frequency table to organize real world data.
- Calculate various types of relative frequencies.
- Make comparisons between two data sets using relative frequencies
- Calculate joint, marginal, and conditional relative frequencies.
- Describe patterns observed in the data. Recognize the association between two variables by comparing conditional and marginal percentages.
Standards Addressed
Math Content Standards
- S.ID.5. Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
Math Practice Standards
- MP.1 Make sense of problems and persevere in solving them.
- MP.2 Reason abstractly and quantitatively.
- MP.3 Construct viable arguments and critique the reasoning of others.
- MP.4 Model with mathematics.
- MP.5 Use appropriate tools strategically
Instructional Approach
The United Nations uses two main indicators to measure the degree to which people in countries around the world have adequate food (and are making progress on Article 25):
- The prevalence (in %) of children <5 who are underweight
- The proportion of adults with body mass index (BMI) <18.5
This lesson is focused on understanding the second indicator: the proportion of adults with body mass index (BMI) <18.5.
Teacher Explanation
- We begin this lesson by asking students:“What is BMI?” Body Mass Index (BMI) is a simple index of weight-for-height that is commonly used to classify adults into categories such as underweight, overweight and obese. A Belgian statistician named Quetelet developed this index over 100 years ago and it is still often used today to determine people’s weight category. In fact, the index has become popularized in gyms and exercise programs.
- BMI is defined as the weight in kilograms divided by the square of the height in meters (kg/m2).
BMI= Weight(kg) / (Height(meters))2
- In the media, BMI is often talked about in the context of overweight and obesity. However, when used as an indicator for human rights (Article 25) the focus is on measuring the degree to which an individual’s BMI is lower than 18.5, which indicates that the person is underweight.
- Project the table below and explain to the students that these are the cut-off points for classifying people’s weight status according to their BMI.
- The United Nations follows these guidelines and therefore uses the proportion of adults with body mass index (BMI) <18.5 as an indicator for the human right of having adequate food. As more people move from the category of underweight to normal range, then the region is making progress in providing adequate food to its citizens.
Classification | BMI(kg/m2) Cut-off points |
Underweight | <18.50 |
Normal range | 18.50 - 24.99 |
Overweight | ≥25.00 |
Obese | ≥30.00 |
Source: Adapted from WHO, 1995, WHO, 2000 and WHO 2004.
BMI = Weight(kg) / (Height(meters))2
- Let’s look more closely at how we figure out the BMI of an individual. (Please note: you will not need to measure your BMI or anyone else in the class).
Example 1
Suppose a person weighs 40 kg, and his/her height is 1.7 meters, what would be his/her BMI? Would that person be classified as underweight?
Demonstrate step by step how you calculated your answer to this question.
Example 2
Project the slide of LeBron James.
Inform students that at the peak of his career, LeBron was 6’8” tall and weighed 250 lbs.
Tell students that together they are going to calculate his BMI.
- Before you begin, write on the board the following conversions units:
1 Meter (m) = 39.36 inches
1 Kilogram (kg) = 2.202 lbs.
- Ask students for some suggestions about how to go about calculating his BMI.
- If needed, provide guiding questions. It is okay to use calculators!
Step 1:
Conversion from U.S. system to SI system
6’8” =80”
80/39.36= 2.03 meters
250 lbs./2.202 =113.53 kg.
Step 2:
Use the BMI formula
BMI= 113.53/(2.03)^2= 27.55
Looking at the BMI classification chart, and using LeBron’s BMI, ask students to classify LeBron into the correct weight category (overweight).
Ask students: Does that make sense?
- Inform students that this is one of many examples in which the BMI classification fails to accurately describe a person. In general, BMI is a crude measure and does not take into account other factors that influence health, such as body frame and muscularity. The BMI does not differentiate between fat and muscle weight so many athletes end up being classified as overweight, and even obese, when in fact they are in good health with very little fat on their body. In addition, remind students that BMI is an indicator designed to categorize adults, NOT children or teens.
- Why use BMI at all?
This is a great opportunity to highlight the difference between population and individuals. On a population basis – when we look at large quantities (e.g. millions) of BMI numbers – it is a useful measure because it actually correlates with health risk related to being underweight or overweight. However, on an individual basis it is more problematic.
Small Group Work
- Divide students into small groups (2-3)
- Distribute Handout#1 and ask them to work together to complete it.
Handout #1
Source: Adapted from WHO, 1995, WHO, 2000 and WHO 2004. 1 Meter (m) = 39.36 inches 1 Kilogram (kg) = 2.202 lbs. Complete the following questions 1. Suppose a woman is 1.5 meters tall and weighs 38kg. a) What is her BMI? b) How much weight does she need to gain for her BMI to reach a normal range? c) Write an equation that represents your answer. (3.625kg) 2. How much weight would she have to lose before she would be classified as severely underweight? How do you know? 3. Suppose a person weighs 150 lbs. and is 6 feet tall, what is his/her BMI? Is s/he underweight? 4. If someone’s weight was doubled, what would happen to his/her BMI? Justify your answer. 5. ** To avoid the conversion you had to do in the previous question, the BMI formula, which is originally in the SI (makes sense as it is an international measurement), was adjusted for the U.S system. The adjusted BMI is defined as the weight in pounds, divided by the square of the height in inches (lbs./inch2) and all that multiplied by a conversion factor of 703. BMI = 703Weight(lbs) / (Height(inch))2 6. How do you think they developed this adjusted formula? How did they determine the conversion factor to be 703? |
All Class Discussion
- Project the questions from Handout #1 one by one and ask volunteers to answer these questions. Make sure to rotate between students from different groups.
- Encourage students to share their answers and be forthright if do not agree with the presenter’s explanation.
Assessment:
Check for student understanding and assess learning through work on Handouts and participation in small and large group discussions.